Introduction

This notebook is the exploratory analysis notebook for the study. Here, I explore, mainly via visualisations, interesting patterns in arrival and departure times of some migratory bird species changing with their wintering latitudes.

Questions

Exploration

Investigating arrival and departure timings

After all our selection and filtering criteria for wintering species of interest, and after filtering data for each species to its wintering latitudinal range (removing latitudes where not purely wintering), we now start the analysis.

Using quantiles (assuming 95%), we determine “true” arrival and departure dates for each species per latitude. For a preliminary visualisation of patterns across species, we visualise this latitudinal trend of arrival (blue) & departure (red) times for all species:

We now calculate metrics for migration timings, such as first northern/southern arrival & departure, and synchronicity which is our primary metric of interest. We describe synchronicity using two (presumably) orthogonal angles: slope (quickness of migration) and tightness (uniformity) across latitudes. (Correlation R^2 cannot be used for the measure of tightness, since for high slope values, R2 becomes low.)

Here are the synchronicity measures (SYNC.SLOPE & SYNC.TIGHT) for a set of illustrative species, followed by updated plots for the same species.

## # A tibble: 50 × 6
##    COMMON.NAME               DATE.TYPE   SLOPE    SE SYNC.SLOPE SYNC.TIGHT
##    <chr>                     <fct>       <dbl> <dbl>      <dbl>      <dbl>
##  1 Cinereous Vulture         DEP        6.21   0.921  -1.60         0.0827
##  2 Bar-tailed Godwit         DEP        3.89   2.60   -1.19        -0.956 
##  3 Brown-breasted Flycatcher DEP        2.47   0.479  -0.795        0.737 
##  4 Black Redstart            DEP        2.21   0.292  -0.696        1.23  
##  5 Blyth's Reed Warbler      DEP        1.86   0.213  -0.548        1.55  
##  6 Red-breasted Flycatcher   DEP        1.53   0.312  -0.373        1.16  
##  7 Lesser Whitethroat        DEP        1.50   0.462  -0.361        0.771 
##  8 Common Chiffchaff         DEP        1.46   0.410  -0.332        0.891 
##  9 Siberian Stonechat        DEP        1.39   0.246  -0.293        1.40  
## 10 Bar-headed Goose          DEP        1.26   0.283  -0.203        1.26  
## 11 Taiga Flycatcher          DEP        0.988  0.300   0.00665      1.21  
## 12 Eurasian Wigeon           DEP        0.795  0.344   0.197        1.07  
## 13 Brown-headed Gull         DEP       -0.766  0.472   0.229        0.750 
## 14 Brown Shrike              DEP        0.519  0.282   0.570        1.27  
## 15 Tufted Duck               DEP        0.511  0.447   0.584        0.806 
## 16 Spotted Redshank          DEP        0.504  0.327   0.595        1.12  
## 17 Greenish Warbler          DEP       -0.459  0.362   0.677        1.02  
## 18 Gray Wagtail              DEP        0.425  0.253   0.745        1.38  
## 19 Green Warbler             DEP        0.363  0.467   0.883        0.762 
## 20 Common Buzzard            DEP       -0.272  0.880   1.13         0.128 
## 21 Greater Spotted Eagle     DEP        0.245  0.254   1.23         1.37  
## 22 Sykes's Warbler           DEP        0.147  0.847   1.67         0.166 
## 23 Western Yellow Wagtail    DEP        0.0612 0.241   2.44         1.42  
## 24 Booted Eagle              DEP       -0.0444 0.250   2.72         1.39  
## 25 Pallid Harrier            DEP        0.0227 0.334   3.31         1.10  
## 26 Blyth's Reed Warbler      ARR       -3.33   0.459  -1.06         0.778 
## 27 Cinereous Vulture         ARR       -2.39   2.38   -0.766       -0.866 
## 28 Green Warbler             ARR       -1.78   0.270  -0.510        1.31  
## 29 Brown-breasted Flycatcher ARR       -1.78   1.02   -0.506       -0.0229
## 30 Western Yellow Wagtail    ARR       -1.73   0.204  -0.481        1.59  
## 31 Pallid Harrier            ARR       -1.62   0.240  -0.423        1.43  
## 32 Sykes's Warbler           ARR       -1.51   0.984  -0.362        0.0157
## 33 Eurasian Wigeon           ARR       -1.35   0.272  -0.266        1.30  
## 34 Common Chiffchaff         ARR       -1.22   0.440  -0.176        0.821 
## 35 Brown-headed Gull         ARR       -1.04   0.533  -0.0368       0.630 
## 36 Bar-tailed Godwit         ARR       -0.997  0.958  -0.000733     0.0428
## 37 Greenish Warbler          ARR       -0.980  0.280   0.0143       1.27  
## 38 Booted Eagle              ARR       -0.976  0.209   0.0177       1.57  
## 39 Brown Shrike              ARR       -0.732  0.160   0.270        1.83  
## 40 Taiga Flycatcher          ARR       -0.722  0.250   0.281        1.39  
## 41 Siberian Stonechat        ARR       -0.705  0.182   0.302        1.70  
## 42 Tufted Duck               ARR       -0.700  0.527   0.308        0.640 
## 43 Red-breasted Flycatcher   ARR       -0.642  0.248   0.384        1.39  
## 44 Lesser Whitethroat        ARR       -0.610  0.255   0.429        1.36  
## 45 Spotted Redshank          ARR        0.552  1.02    0.516       -0.0168
## 46 Common Buzzard            ARR        0.480  0.335   0.637        1.09  
## 47 Black Redstart            ARR       -0.409  0.172   0.779        1.76  
## 48 Gray Wagtail              ARR        0.342  0.209   0.934        1.57  
## 49 Bar-headed Goose          ARR       -0.129  0.146   1.79         1.92  
## 50 Greater Spotted Eagle     ARR        0.0515 0.332   2.59         1.10

All our species can be visualised as occupying a 2-D space governed by the two measures of synchronicity. Based on their occupancy of this space, we can classify their overall synchronicity.

Now will try to combine the two variables into a single index of synchronicity. Relative weights are obtained from PCA of the two variables, and the index is a linear combination of the two. New values and updated graphs below.

## # A tibble: 50 × 7
##    COMMON.NAME            DATE.TYPE SYNC.IND   SLOPE    SE SYNC.SLOPE SYNC.TIGHT
##    <chr>                  <fct>        <dbl>   <dbl> <dbl>      <dbl>      <dbl>
##  1 Bar-tailed Godwit      DEP       -1.12     3.89   2.60   -1.19        -0.956 
##  2 Cinereous Vulture      DEP       -1.08     6.21   0.921  -1.60         0.0827
##  3 Brown-breasted Flycat… DEP       -0.320    2.47   0.479  -0.795        0.737 
##  4 Black Redstart         DEP       -0.0982   2.21   0.292  -0.696        1.23  
##  5 Lesser Whitethroat     DEP       -0.00962  1.50   0.462  -0.361        0.771 
##  6 Common Chiffchaff      DEP        0.0472   1.46   0.410  -0.332        0.891 
##  7 Blyth's Reed Warbler   DEP        0.102    1.86   0.213  -0.548        1.55  
##  8 Red-breasted Flycatch… DEP        0.103    1.53   0.312  -0.373        1.16  
##  9 Siberian Stonechat     DEP        0.233    1.39   0.246  -0.293        1.40  
## 10 Bar-headed Goose       DEP        0.252    1.26   0.283  -0.203        1.26  
## 11 Taiga Flycatcher       DEP        0.378    0.988  0.300   0.00665      1.21  
## 12 Brown-headed Gull      DEP        0.391   -0.766  0.472   0.229        0.750 
## 13 Eurasian Wigeon        DEP        0.466    0.795  0.344   0.197        1.07  
## 14 Tufted Duck            DEP        0.653    0.511  0.447   0.584        0.806 
## 15 Spotted Redshank       DEP        0.757    0.504  0.327   0.595        1.12  
## 16 Greenish Warbler       DEP        0.782   -0.459  0.362   0.677        1.02  
## 17 Brown Shrike           DEP        0.786    0.519  0.282   0.570        1.27  
## 18 Common Buzzard         DEP        0.822   -0.272  0.880   1.13         0.128 
## 19 Green Warbler          DEP        0.846    0.363  0.467   0.883        0.762 
## 20 Gray Wagtail           DEP        0.940    0.425  0.253   0.745        1.38  
## 21 Sykes's Warbler        DEP        1.21     0.147  0.847   1.67         0.166 
## 22 Greater Spotted Eagle  DEP        1.27     0.245  0.254   1.23         1.37  
## 23 Western Yellow Wagtail DEP        2.13     0.0612 0.241   2.44         1.42  
## 24 Booted Eagle           DEP        2.31    -0.0444 0.250   2.72         1.39  
## 25 Pallid Harrier         DEP        2.62     0.0227 0.334   3.31         1.10  
## 26 Cinereous Vulture      ARR       -0.797   -2.39   2.38   -0.766       -0.866 
## 27 Blyth's Reed Warbler   ARR       -0.487   -3.33   0.459  -1.06         0.778 
## 28 Brown-breasted Flycat… ARR       -0.357   -1.78   1.02   -0.506       -0.0229
## 29 Sykes's Warbler        ARR       -0.245   -1.51   0.984  -0.362        0.0157
## 30 Bar-tailed Godwit      ARR        0.0127  -0.997  0.958  -0.000733     0.0428
## 31 Green Warbler          ARR        0.0545  -1.78   0.270  -0.510        1.31  
## 32 Common Chiffchaff      ARR        0.133   -1.22   0.440  -0.176        0.821 
## 33 Pallid Harrier         ARR        0.151   -1.62   0.240  -0.423        1.43  
## 34 Western Yellow Wagtail ARR        0.160   -1.73   0.204  -0.481        1.59  
## 35 Brown-headed Gull      ARR        0.170   -1.04   0.533  -0.0368       0.630 
## 36 Eurasian Wigeon        ARR        0.220   -1.35   0.272  -0.266        1.30  
## 37 Spotted Redshank       ARR        0.351    0.552  1.02    0.516       -0.0168
## 38 Greenish Warbler       ARR        0.405   -0.980  0.280   0.0143       1.27  
## 39 Tufted Duck            ARR        0.411   -0.700  0.527   0.308        0.640 
## 40 Booted Eagle           ARR        0.498   -0.976  0.209   0.0177       1.57  
## 41 Taiga Flycatcher       ARR        0.624   -0.722  0.250   0.281        1.39  
## 42 Red-breasted Flycatch… ARR        0.697   -0.642  0.248   0.384        1.39  
## 43 Lesser Whitethroat     ARR        0.719   -0.610  0.255   0.429        1.36  
## 44 Siberian Stonechat     ARR        0.736   -0.705  0.182   0.302        1.70  
## 45 Brown Shrike           ARR        0.754   -0.732  0.160   0.270        1.83  
## 46 Common Buzzard         ARR        0.779    0.480  0.335   0.637        1.09  
## 47 Black Redstart         ARR        1.08    -0.409  0.172   0.779        1.76  
## 48 Gray Wagtail           ARR        1.13     0.342  0.209   0.934        1.57  
## 49 Bar-headed Goose       ARR        1.83    -0.129  0.146   1.79         1.92  
## 50 Greater Spotted Eagle  ARR        2.13     0.0515 0.332   2.59         1.10
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

There is still some finetuning to be done with the “quickness” metric, i.e., derived from slope. For the most synchronous species with little difference, the values change drastically. Also need to figure out how to appropriately weight the two so that high togetherness is prioritised.

Further try ordinations to understand what factors (wintering, migrating) determine synchronicity of species.